The connection with the language of desirability is now almost immediate, because it is eminently suited for dealing with binary preference statements such as “the gamble \(g\)  is strictly preferred over the gamble \(f\) ”.
In terms of desirability, this simply means that \(g-f\)  is desirable [1]}, [2]}.
By applying this to our interpretation for rejection in terms of preferences, we obtain an equivalent interpretation in terms of desirability: \(f\)  is rejected from \(A_{}\)  if the option set
\(A_{}\ominus f[]{g-f\colon g\in A_{}\setminus {f}}\) 
